Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
574 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22590705 | C2 | semidirect |
| 4. #22586787 | C2 | semidirect |
| 5. #22586232 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 24. #477×C71 | C4 | semidirect |
| 25. #460×C71 | C4 | semidirect |
| 122. Q8×C71 | #104 | semidirect |
| 191. C71 | #9326 | semidirect |
| 196. #477 | Dic71 | semidirect |
| 197. #460 | Dic71 | semidirect |
| 306. Q8 | #14556055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590705 | 2 |
| #22589260 | 2 |
| #22586848 | 2 |
| #22586787 | 2 |
| #22586232 | 2 |
| #22586197 | 2 |
| C71×#3112 | 2 |
| #9326 | 71 |